Ulster were beaten 43-31 by Bordeaux at the Chaban-Delmas Arena to end their Investec Champions Cup run at the last 16 stage.
The Irish team twice equalised after falling behind and finished the match with five tries, but Bordeaux showed outstanding performances even without French talent Louis Bielle-Biarrei, who was on holiday.
Zak Ward scored two tries for Ulster in a frenetic final quarter but the star of the game was his attacking partner Jacob Stockdale, who continually caused problems for the opposition defence.
A thrilling match was kick-started by Damian Penaud, who raced halfway across the pitch to score a brilliant goal in the seventh minute, punishing the opposition for falling behind in the fight for possession against Ulster.
Five strikers, including Ben Tameifuna and Adam Coleman, added tries to give Bordeaux a 21-0 lead, but the visitors responded.
Holding midfielder Tom O'Toole and No.8 Dave McCann both had close-range tries but both came courtesy of creative play, with Stockdale in particular standing out.
However, the situation changed in injury time in the first half when a miscue led to a counter-attack and Bordeaux switched to active play, allowing Romain Bourros to score.
Maxime Luku converted a penalty early in the second half and then the 14 heavyweights showed their physical prowess in close combat when Maxime Lamothe scored.
Ulster were not about to give up and their tenacity was evident on 56 minutes when they displayed excellent interplay in tight spaces and Stockdale set up Nick Timoney, who fired superbly into the left-hand corner.
Thanks to Stockdale and centre Stuart McCloskey, Ulster showed patience and scored a fourth try, with Zak Ward scoring a touchdown to cut the deficit to 12 points.
However, Bordeaux showed their strength again, with Rohan Janse van Rensburg breaking through as his side were changing gears and then Ward punishing their weakness with his second try.
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